Question

1. A bond issued on January 1, 2018 with a face amount of ​$5,000 at 5% has a current price quote of 100. Interest is payable on 7/1 and 1/1. The market rate is 5%. This is a 2 year bond.

What is the amount of the discount or premium? Enter a number value.

2.A bond issued on January 1, 2018 with a face amount of ​$8,000 at 5% has a current price quote of 103. Interest is payable on 7/1 and 1/1. The market rate is 4%. This is a 2 year bond.

What is the amount of discount or premium amortized on 7/1? Enter a number value.

3.A bond issued on January 1, 2018 with a face amount of ​$3,000 at 5% has a current price quote of 102. Interest is payable on 7/1 and 1/1. The market rate is 4%. This is a 2-year bond.

What is the interest expense amount on 7/1? Enter a number value.

Answer 1

1) The premium or discount on issue of bonds is equal to difference between face value of bonds and issue price of bonds. The issue price of bonds will differ from face value of bonds if market rate of interest and interest rate on bonds is different.

In the given case, the face value of bonds and issue price of bonds are same (i.e. $5,000 as current price quote is 100). The market rate and interest rate on bonds are also same (i.e. 5%). Therefore there will be no premium or discount on issue of bonds in the given case.

Premium or Discount = Face Value - Issue price

= $5,000 - $5,000 = $0

2) Issue price of bonds is equal to sum of present value of face value of bonds and present value of interest payments for bonds.

In the given case, the relevant market rate for discounting is 2% (i.e. 4% per year, then For 6 months = 4%*6/12 = 2%).

No. of periods = 2 years*2 semi annual periods = 4 periods

Interest paid in cash for each period = $8,000*5%*6/12 = $200

Issue price of bonds = [Face Value*PVF(4, 2%)]+[Interest paid*PVF(4, 2%)]

= ($8,000*0.923845)+($200*3.8077287)

= $7,391+$762 = $8,153

Face Value of Bonds = $8,000

Premium on issue of bonds = $8,153 - $8,000 = $153

Interest expense for 7/1 = Issue price*market rate = $8,153*4%*6/12 = $163

Premium to be amortized on 7/1 = Cash paid for interest - Interest expense

= $200 - $163 = $37

Therefore the amount of discount or premium amortized on 7/1 is $37.

3) Issue price of bonds is equal to sum of present value of face value of bonds and present value of interest payments for bonds.

In the given case, the relevant market rate for discounting is 2% (i.e. 4% per year, then For 6 months = 4%*6/12 = 2%).

No. of periods = 2 years*2 semi annual periods = 4 periods

Interest paid in cash for each period = $3,000*5%*6/12 = $75

Issue price of bonds = [Face Value*PVF(4, 2%)]+[Interest paid*PVF(4, 2%)]

= ($3,000*0.923845)+($75*3.8077287)

= $2,771.54+$285.58 = $3,057.12 or $3,057 (rounded off)

Face Value of Bonds = $3,000

Premium on issue of bonds = $3,057 - $3,000 = $57

Interest expense for 7/1 = Issue price*market rate = $3,057*4%*6/12 = $61

Therefore the interest expense on 7/1 is $61.